Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition

Singh, Gurjeet; Memoli, Facundo; Carlsson, Gunnar

Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition

Files

091-100.pdf (276.1 KB)

Date

2007

Authors

Singh, Gurjeet
Memoli, Facundo
Carlsson, Gunnar

Publisher

The Eurographics Association

Abstract

We present a computational method for extracting simple descriptions of high dimensional data sets in the form of simplicial complexes. Our method, called Mapper, is based on the idea of partial clustering of the data guided by a set of functions defined on the data. The proposed method is not dependent on any particular clustering algorithm, i.e. any clustering algorithm may be used with Mapper. We implement this method and present a few sample applications in which simple descriptions of the data present important information about its structure.

        @inproceedings{:10.2312/SPBG/SPBG07/091-100
,
booktitle = {Eurographics Symposium on Point-Based Graphics
},
editor = {M. Botsch and R. Pajarola and B. Chen and M. Zwicker
},
title = {{Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition
}},
author = {Singh, Gurjeet and 
Memoli, Facundo and 
Carlsson, Gunnar
},
year = {2007
},
publisher = {The Eurographics Association
},
ISSN = {1811-7813
},
ISBN = {978-3-905673-51-7
},
DOI = {/10.2312/SPBG/SPBG07/091-100
}
}